Abductive Inference Models for Diagnostic Problem-Solving

We now turn to the issue of automating diagnostic problem-solving and briefly survey representative previous work in this area. Such work is substantial, going back to almost the advent of electronic stored-program computers [Reggia85f], and for this reason the material that follows must unfortunately be quite selective. It is organized into three sections. The first section describes some basic concepts of knowledge-based systems. Two important methods that have been used widely to implement knowledge-based diagnostic systems, statistical pattern classification and rule-based deduction, are briefly described. The second section describes another class of systems which we will refer to as association-based abductive systems. These latter models capture the spirit of abductive reasoning in computer models. Two substantial examples of such systems are given and used to introduce the basic terminology of parsimonious covering theory in an informal, intuitive fashion. The third and the final section briefly addresses some practical issues that arise in implementing computational models for diagnosis.

In the probabilistic causal model described in this book, as well as in some others, probabilistic inference is combined with AI symbol processing methods for diagnostic problem-solving. In these models disorders and manifestations (and perhaps intermediate states) are connected by causal links associated with probabilities representing the strength of causal association. A hypothesis, consisting of zero or more disorders, with the highest posterior probability under the given set of manifestations (findings) is typically taken as the optimal problem solution. Conventional sequential search approaches in AI for solving diagnostic problems formulated in this fashion, such as the ones presented in Chapter 5 of this book and the search algorithm in NESTOR [Cooper84], suffer from combinatorial explosion when the number of possible disorders is large. This is because they potentially must compare the posterior probabilities of all or a notable portion of possible combinations of disorders. Pearl’s belief network model adopts a parallel revision method to find global optimal solutions for the special case of singly-connected causal networks within polynomial time of the network diameter [Pearl87]. However, as discussed in Section 5.4, for a non-singly-connected causal network, which is the case for most diagnostic problems, Pearl’s approach requires separate computation for each instantiation of the set of “cycle-cut” nodes, and thus still leads to combinatorial difficulty when this set of cycle-cut nodes is large. All of these problems raise the issue of whether the probabilistic causal model described in this book might be formulated as a highly parallel computation, i.e., as a “connectionist model”, so that combinatorial explosion can be avoided.